Lottery Puzzle

Let's say there's a lottery run once every month that costs $100 to enter. Chance of winning is 1 in 20,000. The prize is 5 million dollars. Should you play this lottery?


  1. Absolutely, if you afford to play it a bunch of times (ie, if the $100 cost is really worth just the money to you. You may not want to play if you're down to your last $100, which you need for an operation or you'll die, since that will change the cost for you)

    Straight up, the expected value is like $250k.

  2. That's assuming everyone gets $5 billion, anyway. If it's split, it is probably not worth it again, as I imagine a lot of people would play at those odds, driving your expected value down to the negatives as ten thousand people win at once. Depends how many people you expect to enter.

  3. I think the interesting wrinkle is, if you commit to playing this lottery, you have less than 6% chance of winning it anytime in your lifetime (say, 100 years). So with a confidence level of some 95%, you're committed to just throwing away $100/month for your whole life. Is that a game you'd really play?

    This came to me the other morning while watching CNBC/ reading a historical site on precious metals that asserted a financial collapse was necessary, but judging from Ancient Rome, might not happen for a few centuries. So it occured to me: Should you bet on commodity metal over fiat currency? Similar overall problem; expected value is in your favor, but almost surely won't payoff in your lifetime.

  4. EDIT: I think I glitched up and should've made the payoff 5 million dollars (not billion). Still expected value in your favor.

  5. You changing the numbers is going to make all of my posts sound like crazy talk.

    In general, if this is the only bet you make it may not be worth it. But if you frequently take options with a positive expected value you'll eventually come out ahead, even if you may not hit an individual one in your lifetime. This would just be another addition to your portfolio.

    For example, if there were a whole bunch of these lotteries, playing them all would work. Or, buying every ticket for this one. If you can buy as many tickets as you like without changing the odds then you will come out ahead.

  6. I officially declare that all the numbers by Legendary Teeth above were absolutely correct at the time of writing. :)